In this paper, a lattice version of Abelian Chern-Simons theory is defined. In order to maintain the Leibniz rule on the lattice and preserve gauge invariance, this proposal introduces the dual lattice and expresses gauge fields on the dual lattice in terms of the gauge fields on the original lattice. Upon gauge transformation, the matter fields on the dual lattice transform as a collection of parton fields on the vertexes of the lattice cell. These treatments circumvents the issue of forward/backward difference, and also avoids the duplication problem. The construction agrees with the continuous theory up to order \(\mathcal {O}(\epsilon ^5)\) , which is higher than the existing constructions. The form of the action is symmetric with respect to the three spacetime dimensions, and the calculation of Wilson loops is straightforward. The Wilson loops are loops of cubes on the lattice, and they can be decomposed into several line loops. This is similar to the idea of treating Wilson loops as ribbons to regularize the framing anomaly[1]}[2]}. When the Wilson loops don't intersect, the expectation value is the same as the Chern-Simons theory in continuous spacetime, and is the related to linking number. Generalization to triangular prism and hexagonal prism lattices are also discussed.
